The parametric generalized fractional nikiforov-uvarov method and its applications†

Abstract

By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The obtained results are applied on the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the Pöschl-Teller potential which play an important role in the fields of molecular and hadronic physics. The special of classical cases are obtained from the fractional cases at α = β = 1 which are agreements with recent works.